A340449 Nonsquare composites n whose smallest prime factor is greater than or equal to n^(2/5).

15, 35, 55, 77, 91, 119, 143, 187, 209, 221, 247, 253, 299, 319, 323, 341, 377, 391, 403, 437, 481, 493, 527, 533, 551, 559, 589, 629, 667, 697, 703, 713, 731, 779, 799, 817, 851, 893, 899, 901, 943, 989, 1003, 1007, 1037, 1073, 1081, 1121, 1139, 1147, 1159, 1189

Offset

1,1

Comments

Referred to as "freak-show composites" by Doug Massey (see link) who noted that they are exceptionally difficult to factor by hand using trial division.

4181, 4183, 4187, 4189 is the lowest sequence of four values in the sequence that differ only in the last decimal digit. The next such sequence begins at 806621.

Ankit Bisain says that for sufficiently large x, there are fewer values in this sequence less than x than there are primes less than x.

Links

Table of n, a(n) for n=1..52.

Quora, What's the definition of a freak-show composite number?

Example

The smallest prime factor of 4189 is 59, which is greater than 4189^(2/5).

Maple

q:= n-> not (isprime(n) or issqr(n) or min(numtheory[factorset](n))^5<n^2):
select(q, [$4..2030])[];  # Alois P. Heinz, Jan 07 2021

Mathematica

nscQ[n_]:=CompositeQ[n]&&!IntegerQ[Sqrt[n]]&&FactorInteger[n][[1, 1]]>= Surd[n^2, 5]; Select[Range[1200], nscQ] (* Harvey P. Dale, Jul 25 2021 *)

Prog

(PARI) isok(n) = (n>1) && !isprime(n) && !issquare(n) && (factor(n)[1, 1]^5 >= n^2); \\ Michel Marcus, Jan 07 2021

Crossrefs

Superset of A006094, except for initial 6 in that sequence.

Subsequence of A089229.

Sequence in context: A187400 A162280 A290781 * A063532 A212331 A067930

Adjacent sequences: A340446 A340447 A340448 * A340450 A340451 A340452

Keyword

nonn

Author

Phil Scovis, Jan 07 2021

Status

approved